Calculate the mle estimate for mean, Applied Statistics

Assignment Help:

Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They received the following scores: 400, 450, 575, 600, and 625.

(a) Assuming a normal distribution, write out the likelihood function for estimating the mean μ and standard deviation σ of the average class score.

(b) Calculate the MLE estimate for μ and the standard deviation (σ) for this class.

(c) What is the value of the log-likelihood function at this estimate?

(d) What is the least-squares estimate for μ and σ in your data? Are there any differences? Why or why not?

(e) Using a likelihood-ratio test, test whether the MLE estimates from the class are significantly different from the national mean of 500 and national standard deviation of 100.

(Hint: Start by plugging those values into your log-likelihood function. Remember you are testing two restrictions).


Related Discussions:- Calculate the mle estimate for mean

Find probability of remaining paint free - ball duel, In a three-cornered p...

In a three-cornered paint ball duel, A, B, and C successively take shots at each other until only one of them remains paint free. Once hit, a player is out of the game and gets no

Statistical process control, Statistical Process Control The variabilit...

Statistical Process Control The variability present in manufacturing process can either be eliminated completely or minimized to the extent possible. Eliminating the variabilit

Main effects and interactions, what is the independent variable in how ener...

what is the independent variable in how energetic do people feel after drinking different types of soft drints?

Find the optimal order quantity, The Maju Supermarket stocks Munchies Cerea...

The Maju Supermarket stocks Munchies Cereal. Demand for Munchies is 4,000 boxes per year and the super market is open throughout the year. Each box costs $4 and it costs the store

Normal curve applications, Replacement times for TV sets are normally distr...

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Find the replacement time that separates the top 20% from the

Job application, .what job can you after offering that course

.what job can you after offering that course

Displacement of a simply supported beam, The displacement of a simply suppo...

The displacement of a simply supported beam subject to a uniform load is given by the solution of the following differential equation (for small displacements); and q is th

Recitilinear motion, velocity of a particle which moves along the s-axis is...

velocity of a particle which moves along the s-axis is given by v=2-4t+5t then find position velocity,acceleration

Assumptions in anova, Assumptions in ANOVA The various populations f...

Assumptions in ANOVA The various populations from which the samples are drawn should be normal and have the same variance. The requirement of normality can be discarded if t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd